Holt Algebra 1 5-1 Identifying Linear Functions Warm Up 1. Solve 2x – 3y = 12 for y. 2. Graph for...

Holt Algebra 1

5-1 Identifying Linear Functions

Warm Up 1. Solve 2x – 3y = 12 for y.

2. Graph

for D: {–10, –5, 0, 5, 10}.

Holt Algebra 1


Give the domain and range of each relation.

–4

–1

01

2

6

5

xy

x y

1 1

4 4

8 1 : /1 5D x x : / 3 4R y y

: 1, 2,5,6D x : 4, 1,0R y

: 1, 4,8D x : 1, 4R y

Holt Algebra 1


Students will be able to: Identify linear functions and linear equations and graph linear functions that represent real-world situations and give their domain and range.

Learning Target

Holt Algebra 1


The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight line. A function whose graph forms a straight line is called a linear function.

Holt Algebra 1


Identify whether the graph represents a function. Explain. If the graph does represent a function, is the function linear?

The graph is a because every input

has one and only one outpu

function

linear funct

t. The graph is a

because it forms a straight ion line.

Holt Algebra 1




has one and only one output. The graph is not

a linear function because it does not form a

straigh

function

t line.

Holt Algebra 1



The graph is not a function.

Holt Algebra 1




has one and only one outpu

function

linear funct

t. The graph is a

because it forms a straight ion line.

Holt Algebra 1



The graph is not a function.

Holt Algebra 1


In a linear function, a constant change in x corresponds to a constant change in y.

Holt Algebra 1


Tell whether the set of ordered pairs satisfies a linear function. Explain.

{(0, –3), (4, 0), (8, 3), (12, 6), (16, 9)}

4

3

the set satisf lineies a .ar function

x

y

Holt Algebra 1


{(–4, 13), (–2, 1), (0, –3), (2, 1), (4, 13)}

Tell whether the set of ordered pairs satisfies a linear function. Explain.

2

the set is n liot a near funct .ion

x

y DNE

Holt Algebra 1


Tell whether the set of ordered pairs {(3, 5), (5, 4), (7, 3), (9, 2), (11, 1)} satisfies a linear function. Explain.

2

1

the set satisf linear functionies a .

x

y

Holt Algebra 1


Another way to determine whether a function is linear is to look at its equation. A function is linear if it is described by a linear equation. A linear equation is any equation that can be written in the standard form shown below.

Holt Algebra 1


Notice that when a linear equation is written in standard form

• x and y both have exponents of 1.• x and y are not multiplied together.• x and y do not appear in denominators, exponents, or radical signs.

For any two points, there is exactly one line that contains them both. This means you need only two ordered pairs to graph a line.

Holt Algebra 1


Tell whether the function is linear. If so, graph the function.

x = 2y + 42y2y

2 4x y

the function lin is .ear

y

xyx04

20

Holt Algebra 1



xy = 4



the function i ls not .inear

Holt Algebra 1

5-1 Identifying Linear FunctionsTell whether the function is linear. If so, graph the function.

y = 5x – 9

5x5x5 9x y

the function lin is .ear

y

xyx0

9 / 590

Holt Algebra 1

5-1 Identifying Linear FunctionsTell whether the function is linear. If so, graph the function.

y = 12 0 12x y

the function

l is .inear

y

x

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y = 2x



the function i ls not .inear

Holt Algebra 1


For linear functions whose graphs are not horizontal, the domain and range are all real numbers. However, in many real-world situations, the domain and range must be restricted. For example, some quantities cannot be negative, such as time.

Holt Algebra 1


Sometimes domain and range are restricted even further to a set of points. For example, a quantity such as number of people can only be whole numbers. When this happens, the graph is not actually connected because every point on the line is not a solution. However, you may see these graphs shown connected to indicate that the linear pattern, or trend, continues.

Holt Algebra 1


The relationship between human years and dog years is given by the function y = 7x, where x is the number of human years. Graph this function and give its domain and range.

HW pp. 300-302/15-25, 30-54even,60

y

x1 2 3 4 5 6 7 8

714212835424956

yx04

028

: / 0D x x : / 0R y y

Holt Algebra 1 5-1 Identifying Linear Functions Warm Up 1. Solve 2x – 3y = 12 for y. 2. Graph for...

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